Integral Bounds Determination in Spherical Coordinates

[DHB_Integral]

Homework Statement

How to determine the integral bounds of phi in spherical polar coordinates. Please see my exact question at the end of page 2 of 2 in attachments.

Homework Equations

Please see my attachments

The Attempt at a Solution

Please see my attachments.

 

[DHB_Integral]

I just tried out the integral bounds of phi , it can work getting the correct result. but It cannot convince myself in terms of the bounds of phi, based on the graph on page 1, it should be equal to pi/4. So, how to prove the bounds of phi? Please help with question.

Thanks a lot in advance.